In a non-conventional lap tool, i.e., not a stiff tool nor a conformable tool, and related method for grinding/polishing a substrate surface, includes a rigid base plate and attached work surface to define a cavity containing a non-Newtonian fluid. The non-Newtonian fluid behaves as a solid when the work surface is subjected to high shear stress, i.e., rapid tool stroke, yet behaves like a liquid when the tool is moved around the substrate surface when the shear stress of the work surface is low. A diaphragm can be used to further define the cavity and to seal within the non-Newtonian fluid therein.